Walsh series analysis in optimal control

Chen, C. F.; Hsiao, C. H.

doi:10.1080/00207177508922043

Cited by 71 publications

(18 citation statements)

References 6 publications

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“…The time-optimal control of singular systems was analyzed by Wansheng Tang et al [15] Many models that enter into this framework can be found in practice and, in particular, in the existing literature. Among these we can mention: Chen and Hsiao [5], Chen and Shih [6], applied Walsh series to study the problem of optimal control of time-invariant and time-varying linear systems. It is to be noted that from the study of past literature that Cobb [7] and Pandolfi [13] seems to have been the first authors to consider the optimal regulator problem of continuous time singular systems.…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of the time invariant optimal control of singular systems using Adomian decomposition method

Sekar¹,

Kavitha²

2014

ams

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This paper deals with the implementation of Adomian Decomposition Method (ADM) to solve the optimal control problem of linear time invariant singular systems with a quadratic cost functional. The idea is that the states and the input are expressed in terms of ADM. The method simplifies the system of state equations into a set of algebraic equations which can be solved using a digital computer. Illustrative example is included to demonstrate the validity and applicability of the technique.Mathematics Subject Classification: 65L05, 65L80

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Section: Introductionmentioning

confidence: 99%

Numerical investigation of the time invariant optimal control of singular systems using Adomian decomposition method

Sekar¹,

Kavitha²

2014

ams

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“…Generalized delay systems are important to be investigated. Orthogonal functions or polynomials such as Walsh [1], block-pulse functions [3] Chebyshev [2], Laguerre [4], Legendre [5], Fourier [8], and hybrid functions [6,7,10,12] are developed for application. In the paper [9], Legendre wavelets were used to solve the variational problems.…”

Section: Introductionmentioning

confidence: 99%

A numerical approach of optimal control for generalized delay systems by general Legendre wavelets

Wang

2009

International Journal of Computer Mathematics

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A general Legendre wavelets approach is presented. The delay function is expanded by general Legendre wavelets. The general operational matrix of integration is introduced. By the general Legendre wavelets, the linear-quadratic problem of generalized delay systems are transformed into the optimization problem of multivariate functions. The approximate solutions of the optimal control and state as well as the optimal value of the objective functional are derived. The numerical examples demonstrate that the algorithms are valid.

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“…The Walsh operational matrix based method in continuous system introduced by Chen and Hsiao [1] have been successfully used in the solution of state space equation [1], identification [2], optimization [3][4][5], solution of variational problems [6], analysis of delay differential equations [7], etc. Since then many operational matrices based on various orthogonal functions such as Laguerre [8,9], Legendre [10], Chebyshev [11] and Fourier [12] have been developed.…”

Section: Introductionmentioning

confidence: 99%